Named in 1952 after John Bromleigh (fl. 1432), abbot of Bermondsey from 1432 to 1473. One of three blocks of flats on the Sydenham Hill Estate named after abbots (or priors) of Bermondsey Abbey (or Priory), lord of the manor of Dulwich from 1127 to the Dissolution of the Monasteries in 1538. The others are Attleborough Court and Dunton Court.